# Differentiation Questions and Answers

Math

Differentiation Solutions

In a tidal river, the time between high tide and low tide is 5.8 hours. At high tide the depth of the water is 18.4 feet, while at low tide the depth is 4.8 feet. Assume the water depth is a

Math

Differentiation Solutions

A trash company is designing an open-top, rectangular container that will have a volume of 6655 ft. The cost of making the bottom of the container is $5 per square foot, and the cost of the sides is

Calculus

Differentiation Solutions

The slope of the line given by the parametric equations x =12t-11 and y = 6t+13 is: a. 2 b.3 c. 6 d. 1/2 e.1/3

Math

Differentiation Solutions

If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p = 66- x/36. How many bolts must be sold to maximize revenue? A. 1,188 bolts B. 2,376

Math

Differentiation Solutions

A ball is thrown into the air from a tree house and eventually lands on the ground. The equation below shows the distance in feet the ball is from the ground seconds after it is thrown. How high will

Math

Differentiation Solutions

To measure the physical properties of cells, a piezoelectric probe is used. The force applied by the probe is compared against how much the cell deforms. If F is the force applied by the probe, and

Math

Differentiation Solutions

Which step is necessary in verifying that InB + 3 = -3t is a solution to dB/dt=-3B? a)e^InB + e^3 = e^-3t b)1/B (dB/dt)=-3 c) edB = -3dt d)∫(InB+3)dB = ∫-3t dt

Math

Differentiation Solutions

Let f be a twice-differentiable function with derivative given by f'(x) = 4x³ - 24x². (A) Find the x-coordinate of any possible critical points of f. Show your work. (B) Find the x-coordinate of any

Math

Differentiation Solutions

For the differential equation dy/dx=-( e^-x)-3x^2 A): Find a general solution. Show all your work. B): Verify the solution. Show all your work.

Math

Differentiation Solutions

Suppose that f(4) = 3, g(4) = 4, f'(4) = -5, and g'(4) = 2. Find h'(4). (a) h(x) = 3f(x) + 2g(x) h'(4) = (b) h(x) = f(x)g(x) h'(4) = (c) h(x) =f(x)/g(x) h'(4) = (d) h(x) =(g(x))/(f(x) + g(x))

Math

Differentiation Solutions

Jenae tosses a quarter from the shore into the St. Johns River. The distance h(t), in feet, from which the quarter is above the water is modeled by the expression h(t) = -16t2+64t where t represents